Problem Statement

Consider strings of length N consisting of A, B, and C.
Among them, find the number of strings that satisfy the following condition, modulo 2:

• Let S_i be the string formed by the first i characters of S.
  Also let A_i, B_i, and C_i be the numbers of A's, B's, and C's in S_i, respectively.
  For all i such that $1 \le i \le N$, the following holds:
• $A_i-B_i \le X$
• $B_i-C_i \le Y$
• $C_i-A_i \le Z$

You have T test cases to solve.

Input

Input is given from Standard Input in the following format:
T
$\mathrm{case}_1$
$\mathrm{case}_2$
$\vdots$
$\mathrm{case}_T$

Each case is in the following format:
N X Y Z

Output

For each case, print the answer.

Constraints

• $1 \le T \le 10$
• $1 \le N \le 10^9$
• $0 \le X,Y,Z \le 10^9$
• All values in input are integers.

Sample Input 1

1
3 2 1 0

Sample Output 1

0

8 strings satisfy the condition: AAB,AAC,ABA,ABC,ACA,ACB,BAA,BAC.
Therefore the answer is 0.

Sample Input 2

10
1 22 9 92
14 7 74 39
23 50 8 6
93 40 9 60
68 8 47 64
11 68 18 24
3 26 54 8
46 17 90 86
86 76 45 55
80 68 79 62

Sample Output 2

1
0
0
0
1
1
1
0
1
0

见题面 Input 部分

见题面 Output 部分